An aspect that has received less attention, however, is whether constrained OCO algorithms can be assisted by predictions for the next-round functions \(f_t\)  and \(g_t\) . Such information can be provided by a pre-trained model that uses incomplete data and hence cannot be fully trusted – yet, can still assist the online algorithm. Leveraging predictions to improve learning algorithms is attracting increasing interest and has many practical applications, e.g., in data caching [1]}; online rent-or-buy problems [2]}; and in scheduling algorithms [3]}, among other areas. In this context, a key challenge is that the predictions might exhibit time-varying and unknown accuracy, which, furthermore, may vary across the cost and constraint functions. This confounds their incorporation in online learning algorithms and raises the question: how much can predictions improve the performance of constrained OCO algorithms and how can we accrue these benefits in the presence of inaccurate, potentially even adversarial, predictions?
